An Analog of the Salem-Zygmund Theorem for Orthogonal Polynomials on the Unit Circle

  • Peihan Yu University of Wisconsin-Madison

Abstract

In this note, I study the result and proof of the classical Salem-Zygmund Theorem. I apply the method to random orthogonal polynomials on the unit circle. The goal is to find the distribution of M, the sup norm of  suitably defined random polynomial orthogonal on the unit circle. In my proof, I use Bernstein and Chebyshev inequalities  to achieve this goal. I find that for fixed large κ, the probability of M > κ drops significantly as the degree n of the orthogonal polynomial grows.

Published
2019-02-04
How to Cite
YU, Peihan. An Analog of the Salem-Zygmund Theorem for Orthogonal Polynomials on the Unit Circle. Minnesota Journal of Undergraduate Mathematics, [S.l.], v. 4, n. 1, feb. 2019. ISSN 2378-5810. Available at: <https://mjum.math.umn.edu/index.php/mjum/article/view/58>. Date accessed: 24 apr. 2019.
Section
Articles